应用哈特曼-夏克波前传感器测量大气湍流参数

对非科尔莫戈罗夫（Kolmogorov）湍流情况,在利用哈特曼－夏克（Hartmann-Shack)波前传感器的波前斜率测量原理并结合其时空结构及相关分析的基础上,提出了一种应用斜率结构－相关函数和斜率归一化相关系数测量大气湍流参数β（归一化相位空间功率谱指数下降因子）和ρ0（大气湍流强度）的新方法。利用这种方法对1km激光水平大气传输实验数据进行了分析。     

激光大气水平传输湍流畸变波前的功率谱分析I:波前整体倾斜与泰勒频率

利用自适应光学系统的哈特曼 (Hartmann)波前传感器 ,测量了激光实际大气水平传输湍流畸变波前中整体倾斜像差的时间功率谱 ,发现功率谱谱形与科尔莫戈罗夫 (Kolmogorov)湍流理论不完全符合。建立了一种根据实际测量的整体倾斜功率谱估测自适应光学系统倾斜镜需要的控制带宽大小和大气湍流的泰勒 (Tyler)频率指标的方法。     

激光大气水平传输湍流畸变波前的功率谱分析I：波前整体倾斜与泰 …

利用自适应光学系统的哈特曼（Ｈａｒｔｍａｎｎ）波前传感器,测量了激光实际大气水平舆湍流畸变波前中整体倾斜像差的时间功率谱,发现功率谱谱形与科尔莫戈罗夫（Ｋｏｌｍｏｇｏｒｏｖ）湍流理论不完全符合,建立了一种根据实际测量的整体倾斜功率谱估测自适应光学系统斜镜需要的控制带宽大小和大气湍流的泰勒（Ｔｙｌｅｒ）频率指标的方法。     

对流湍流池Fried相干长度的光学结构

利用不同的方法，测量并比较了用自适应光学补偿实验的对流湍流池的相干长度，给出到达角起伏谱和起伏方差的概率分布，结果表明，在对流湍流池中，光束的到达角起伏谱满足“－８／３”幂，由于相位起伏服从正态分布，因此到达角起伏的方差呈Ｘ＾２分布，到达角起伏在水平和垂直方向上的谱完全一致表明了湍流池湍流的各向同性特征，相干长度与对流湍流池上下温差的实验结果，符合以往对流湍流池的流体力学和热力学相心关系。     

湍流大气传输高斯谢尔光束的到达角起伏

研究了在弱大气湍流起伏环境下以窄带宽高斯谢尔光束为激光光源的大气通信问题,分析了大气湍流强度和光源空间相干度对通信光束到达角起伏的影响.采用窄带宽光场的交叉谱密度函数代替光场互相干函数的近似方法和采用包含大气湍流内外尺度的简化折射率谱密度函数,得出了湍流大气中传输高斯谢尔光束的波结构函数(WSF) 和到达角起伏方差解析近似关系.分析表明,光源的空间相干度和传输光束的湍流扩展是影响高斯谢尔光束的相位起伏结构函数和传输光束到达角起伏的重要因素.     

低阶模式校正自适应光学系统的补偿效果分析

引入规格化的相位谱「不一定为科尔莫戈罗夫（Ｋｏｌｍｏｇｏｒｏｖ谱」,推导了大气湍流相位结构函数、低阶模式校正后的残余相位结构函数以及长曝光光学传递函数（ＬＴＦ）。分别给出了在各种不同大气湍流强度ρ０,不同相位谱空间频率的指数下降因子ρ时,大气湍流相位波前低阶模式完全校正后和倾斜部分校正时的长曝光光学传递函数（ＯＴＦ）、长曝光斯特列尔（Ｓｔｒｅｈｌ）比和半高全宽（ＦＷＨＭ）的数值计算结果。     

激光实际大气水平传输湍流畸变波前的功率谱分析II:波前相位与格林伍德频率

分析了整体倾斜像差去除前后大气湍流畸变波前相位的功率谱。在激光实际大气水平传输实验中 ,利用 6 1单元自适应光学系统的哈特曼波前传感器 ,测量和分析了大气湍流畸变波前相位的功率谱。还建立了一种根据实际测量的波前相位功率谱数据估测自适应光学系统变形镜需要控制带宽大小和大气湍流格林伍德 (Greenwood)频率的方法。     

激光实际大气水平传输湍流畸变波前的功率谱分析Ⅱ: 波前相位与格林伍德频率

分析了整体倾斜像差去除前后大气湍流畸变波前相位的功率谱。 在激光实际大气水平传输实验中, 利用61单元自适应光学系统的哈特曼波前传感器, 测量和分析了大气湍流畸变波前相位的功率谱。 还建立了一种根据实际测量的波前相位功率谱数据估测自适应光学系统变形镜需要控制带宽大小和大气湍流格林伍德(Greenwood)频率的方法。     

光束在强湍流区中传播的到达角起伏

 基于修正Rytov理论，导出了适用于强湍流区的无限平面波和球面波的到达角起伏方差表达式及其功率谱表达式，分析了散射盘对到达角起伏的影响。研究结果表明：导出的方差表达式在弱湍流区也适用，随着Rytov方差的增加到达角起伏趋于饱和；高频功率谱的下降速度随着散射盘尺度的增加而增加。     

根据到达角协方差测量大气湍流外尺度

通过湍流大气中光波相位结构函数得到两点间的到达角协方差与大气湍流外尺度的关系,并利用差分到达角方差进行了归一化,进而得到大气湍流外尺度和差分到达角方差及到达角协方差的表达式。采用四孔到达角起伏测量仪进行了近地面水平路径的实验,测量结果表明在离地面6 m的高度上,湍流外尺度在4 m左右,并随时间变化,不同方向的测量结果有一些差别。     

大气湍流波前低阶模式的时间功率谱分析

引入规格化的相位谱,推导了大气湍流波前低阶模式（Ｚ－倾斜和Ｇ－倾斜、离焦、像散以及彗差）的时间功率谱,并就水平大气传输、星体目标观测、空间目标监测等几种情况作了实际的数值计算及分析,此外还给出实验结果,分析结果表明：对于水平大气传输模式,倾斜功率谱曲线的低频阶段的指数下降因子为４／３－６β／１１（β为相位谱空间频率的指数下降因子）,离焦、像散和彗差项的功率谱低频段指数下降因子为０;水平大气传输工作     

Effects of low-order atmosphere-turbulence aberrations on the entangled orbital angular momentum states

Based on Zernike-model expansion of turbulence phase aberrations and non-Kolmogorov spectrum model of index-of-refraction fluctuation, we analyze the effects of low-order Zernike turbulence aberrations on orbital angular momentum (OAM) entanglement states in a weak fluctuation region. The signal photon detection probability of OAM entanglement states propagating in a slant turbulence channel with non-Kolmogorov turbulence Z-tilt, defocus, astigmatism, and coma aberrations are modeled, respectively. The results demonstrate that turbulence Z-tilt aberration is the dominant aberration, coma is the second, and astigmatism is the third, but that the defocus aberration has no impact on the detection probability. As the power-law exponent of the non-Kolmogorov spectrum increases from 3 to 4, the detection probability decreases.     

Effect of the outer scale on the angle of arrival variance for free-space-laser beam corrugated by non-Kolmogorov turbulence

It is well known that atmospheric turbulence causes significant variations of the arrival angle of laser beams used in free-space communications. Usually, angle-of-arrival fluctuations of an optical wave in the plane of the receiver aperture is calculated by Kolmogorov’s power spectral-density model. Unfortunately, recently increasing experimental evidence has shown that atmospheric turbulence statistics does not obey Kolmogorov’s power spectrum model in some parts of the troposphere and stratosphere. These experiments have prompted investigations of the optical-wave propagation through atmospheric turbulence described by nonclassical power spectra. In this paper, employing a new approach and considering a non-Kolmogorov power spectrum with a generalized power law instead of the constant standard power-law value 11/3 and a generalized amplitude factor instead of the constant value 0.033, we derive the variances of the angle-of-arrival fluctuations of the plane and spherical waves in a weak turbulence for the horizontal path. The concise closed-form expressions are obtained and used to analyze the influence of spectral power-law variations on the angle-of-arrival fluctuations. In addition, the outer scale effect is also analyzed.     

梯度倾斜相关测量水平C_n~2和横向风速廓线的理论与仿真研究

根据Rytov近似以及泰勒湍流冻结假设,推导出以不同距离的前向散射光为信标的水平路径上梯度倾斜角的相关表达式.基于该表达式,在理论上提出了计算湍流强度与横向风速的新方法,并通过数值仿真对该方法进行了初步验证.结果表明,在5%高斯误差情况下,大气折射结构常数和风速的计算结果与理论真值在整体变化上具有较好的一致性,线性相关系数分别能达到0.8与0.9.该方法能够得到不同湍流与风速条件下的湍流强度廓线以及风速廓线,为反演大气湍流强度以及风速提供了一种新思路.     

Phase compensation in non-Kolmogorov atmospheric turbulence

Zernike polynomial decompositions are used for investigating phase distortion induced by atmospheric turbulence in optical systems. Closed-form expression of the Zernike-coefficient variances is derived. The finite size of the receiver aperture is analyzed using the filter function which is also particularly effective in the theoretical analysis of lower-order aberrations like tilt terms and piston-removed phase variance. The outer scale of the non-Kolmogorov turbulence is considered. The result shows that the effect of finite outer scale attenuates low-order Zernike mode of optical distortion and longer outer scale can lead to more energy in the tilt terms. The generalized exponent can only enhance tilt terms and attenuate other Zernike modes of optical distortion. Further, for different outer scale and generalized exponent, the residual phase variance decreases with more modes of phase compensation.     

相位板装配倾斜对波前编码系统点扩散函数的影响

分析了装配误差引起的相位板倾斜对波前编码系统的影响,通过坐标变换推导了相应条件下的广义光瞳函数。结果表明：倾斜因子对系统的相位板系数具有放大效果,其随倾斜角绝对值的增大而增大,而与倾斜角的正负无关。相位板倾斜会放大系统点扩散函数包络面的两条直角边,相应地降低其光学传递函数值。在子午倾斜的条件下,子午方向的相位板系数放大效果大于弧矢方向,从而导致点扩散函数包络面在子午方向的放大效果大于弧矢方向,子午方向光学传递函数值的降低效果大于弧矢方向。采用MATLAB以及商用光学软件进行仿真实验,验证了上述结论。     

Measuring the power-law exponent of an atmospheric turbulence phase power spectrum with a Shack Hartmann wave-front sensor

For non-Kolmogorov turbulence we develop a differential angle-of-arrival fluctuation coefficient, which is the ratio between the transverse and longitudinal differential angle-of-arrival variances, and a slope structure-correlation coefficient, which is the ratio between the transverse and longitudinal differences of the slope correlation function and the slope structure function, to measure the power-law exponent of a phase power spectrum with a Shack-Hartmann wave-front sensor: The differential arrival-of-angle fluctuation coefficient and the slope structure-correlation coefficient are both related to power-law exponent beta and are independent of strength parameter rho(0) of the turbulence. We compare the methods developed and use them to evaluate beta in recently completed horizontal atmospheric experiments for 1000-m laser beam propagation.     

Interacting gaps model,dynamics of order book,and stock-market fluctuations

Inspired by order-book models of financial fluctuations, we investigate the Interacting gaps model, which is the schematic one-dimensional system mimicking the order-book dynamics. We find by simulations the power-law tail in return distribution, power-law decay of volatility autocorrelation with exponent 0.5 and Hurst exponent close to 1/2. Surprisingly, when we make a mean-field approximation, i.e. replace the one-dimensional system by effectively infinite-dimensional one, we obtain analytically the return exponent 5/2, in perfect accord with one-dimensional simulations.